I have some older games and programs I still enjoy but I can not run them with Display 1 as my primary as all my games and programs will use the High res setting for its default menus and such which makes them all compacted and unusable.

I want to have certain games and programs work on Display 2, and to use Display 2's resolution and settings as the base resolution.

An example, Dungeons and Dragons Online, older MMO title. It benefits greatly from the 980 ti graphics card I use to run 4k games on Display 1, but none of the menus in the launch menu (pre game) are readable or useable. So this program needs to only recognize Display 2 as its display and run in 1080p on Display 2 without screwing up Display 1's high resolution.

I essentially want to use both monitors as if they were entirely separate computers but run off the same hardware and software, windows 10.

What exactly programs besides games do you need to open on the monitor 2? Actual Multiple Monitors has the feature that let you set where the particular windows will be placed after opening. This feature is called "Move to monitor" and you can enable it here: Configuration module > Window Setings > Particular Specific Settings/Default Settings > Startup section > Move to monitor.

This feature works for the most applications, but it can't make fullscreen games open on other monitors than primary. You can make particular game open on other monitor if the game itself has this option. So, it seems that the best solution for you in this situation is to make your Display 2 primary monitor.